Bones with python: emulate armature with constraints
In short, no, Blender does not support a bone system like that. Blender uses the common approach where a bone's entire transformation matrix defines the coordinate system for their children. What I would suggest is to dive into the math required and rewrite the bone transformations from your system to a matrix that Blender would understand. I think this approach would be easier and saner than trying to emulate your bone system in Blender.

TL;DR: convert your data to Blender's model, rather than trying to force Blender to mimick your model.


  Also there is this restriction in blender that the tail of a bone needs to always point into the direction of its child.


That statement is only true if you keep the "Connected" property of the bone at its default value True. Just uncheck that checkbox and you can move the bone without affecting its parent orientation.